Finite Group Databasebeta

← #32986088

Subgroups — #32986088

Order 18688.

388 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618316C211yesmaximal, characteristic
2#22609785C211yesmaximal, characteristic
3#22609679C211yesmaximal, characteristic
4#22607813C211yesmaximal, characteristic
5#22607813C211yesmaximal, characteristic
6#22607812C211yesmaximal, characteristic
7C73×#1295C211yesmaximal, characteristic
8C2×#14556520—21no—
9C2×#14556502C2211yescharacteristic
10C2×#14556502C2211yescharacteristic
11#17988486C411yescharacteristic
12#17988486C411yescharacteristic
13#17988483C411yescharacteristic
14#17988483C411yescharacteristic
15#17988474—21no—
16#17988474—21no—
17#17988470—21no—
18#17988470—21no—
19#17988453C2211yescharacteristic
20C42×Dic73C2211yescharacteristic
21#17988341—21no—
22#17988341—21no—
23#17988341—21no—
24C2×#97×C73C2211yescharacteristic
25C2×#97×C73C2211yescharacteristic
26#382×C73C2211yescharacteristic
27C22×#10596831—21no—
28C22×#10596831—21no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73C2×C411yescharacteristic
32C2×C4⋊Dic73C2×C411yescharacteristic
33C2×#11924007—21no—
34C2×#11924007—21no—
35C2×C4×Dic73C2×C411yescharacteristic
36C2×C4×Dic73C2×C411yescharacteristic
37C2×C4×Dic73D411yescharacteristic
38C2×C4×Dic73D411yescharacteristic
39C2×C4×Dic73D411yescharacteristic
40C2×C4×Dic73D411yescharacteristic
41#14556520—24no—
42#14556502—21no—
43#14556502—21no—
44#14556502—21no—
45#14556502Q812yes—
46#14556498—21no—
47#14556498—21no—
48#14556498—21no—
49#14556498—21no—
50#14556498—21no—
51#14556498—21no—
52C22×C8×C73—21no—
53C22×C8×C73—21no—
54C2×C4⋊C4×C73C2×C411yescharacteristic
55C2×C4⋊C4×C73C2×C411yescharacteristic
56C2×C42×C73C2311yescharacteristic
57#97×C73—21no—
58#97×C73—21no—
59#97×C73—21no—
60#97×C73Q812yes—
61#95×C73—21no—
62#95×C73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C22×Dic73C22⋊C411yescharacteristic
66C22×Dic73C22⋊C411yescharacteristic
67C22×Dic73C22⋊C411yescharacteristic
68C22×Dic73C22⋊C411yescharacteristic
69C2×#10596831—22no—
70C2×#10596831—22no—
71C2×#10596831—41no—
72C2×#10596831—41no—
73C2×#10596831—41no—
74C2×#10596831—41no—
75C4⋊Dic73—42no—
76C4⋊Dic73—42no—
77C4⋊Dic73—41no—
78C4⋊Dic73—41no—
79#11924007—42no—
80#11924007—42no—
81C4×Dic73—22no—
82C4×Dic73—41no—
83C4×Dic73—41no—
84C4×Dic73—41no—
85C4×Dic73—41no—
86C4×Dic73—41no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73C22×C411yescharacteristic
90C22×C4×C73C2×D411yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92C2×C8×C73—22no—
93C2×C8×C73—22no—
94C2×C8×C73—41no—
95C2×C8×C73—41no—
96C2×C8×C73—41no—
97C2×C8×C73—41no—
98C4⋊C4×C73—41no—
99C4⋊C4×C73—41no—
100C42×C73C2×Q811yescharacteristic
101C42×C73C2×Q811yescharacteristic
102C42×C73#4111yescharacteristic
103C42×C73#4111yescharacteristic
104C23×C73C2×C22⋊C411yescharacteristic
105C2×C4×C73—21no—
106C2×C4×C73—21no—
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—41no—
112C2×C4×C73—41no—
113C2×C4×C73—41no—
114C2×C4×C73—41no—
115C2×C4×C73—41no—
116C2×C4×C73—41no—
117C2×C4×C73C4×Q811yescharacteristic
118C2×C4×C73C4×Q811yescharacteristic
119C2×C4×C73C22⋊Q811yescharacteristic
120C2×C4×C73C22⋊Q811yescharacteristic
121C2×C4×C73#12411yescharacteristic
122C2×C4×C73C4⋊Q811yescharacteristic
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—21no—
130C2×Dic73—21no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—41no—
135C2×Dic73—41no—
136C2×Dic73—41no—
137C2×Dic73—41no—
138C2×Dic73—41no—
139C2×Dic73—41no—
140C2×Dic73#10412yes—
141C8×C73—42no—
142C8×C73—42no—
143#10596831—42no—
144#10596831—42no—
145C22×C73#39111yescharacteristic
146C22×C73#41311yescharacteristic
147C22×C73#41311yescharacteristic
148C22×C73C2×#10411yescharacteristic
149C22×C73#42111yescharacteristic
150C22×C73#42111yescharacteristic
151C22×C73#42111yescharacteristic
152C4×C73—21no—
153C4×C73—21no—
154C4×C73—21no—
155C4×C73—21no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—81no—
159C4×C73—81no—
160Dic73—22no—
161Dic73—41no—
162Dic73—41no—
163Dic73—41no—
164Dic73—81no—
165Dic73—81no—
166#9893—731nomaximal, Sylow
167C2×C73#152911yescharacteristic
168C2×C73#153211yescharacteristic
169C2×C73#153511yescharacteristic
170C2×C73#153511yescharacteristic
171C2×C73#198611yescharacteristic
172C2×C73#199511yescharacteristic
173C2×C73#199811yescharacteristic
174#2864—731no—
175#1767—731no—
176#1745—731no—
177#1295—731no—
178#1295—731no—
179#1295—731no—
180#1295D7311yescharacteristic
181C73#989311yescharacteristic, complemented, Sylow
182C2×C4⋊C8—1461no—
183C2×#97—731no—
184C2×#97—731no—
185C2×#97C2×D7311yescharacteristic
186C2×#97C2×D7311yescharacteristic
187#389—731no—
188#389—731no—
189#389—731no—
190#389—731no—
191#387—1461no—
192#387—1461no—
193#387—1461no—
194#387—1461no—
195#382—731no—
196#382C2×D7311yescharacteristic
197C43—731no—
198#336—1461no—
199#336—1461no—
200#336—1461no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—1461no—
204C22×C8—1461no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—731no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4—1461no—
211C2×C4⋊C4C4×D7311yescharacteristic
212C2×C4⋊C4C4×D7311yescharacteristic
213C2×C42—731no—
214C2×C42—731no—
215C2×C42—731no—
216C2×C42—731no—
217C2×C42—731no—
218C2×C42—731no—
219C2×C42C22×D7311yescharacteristic
220C4⋊C8—1464no—
221#97—21no—
222#97—21no—
223#97—21no—
224#97—732no—
225#97—1461no—
226#97—1461no—
227#97—1461no—
228#97Dic14612yes—
229#95—21no—
230#95—21no—
231#95—1461no—
232#95—1461no—
233#95—1461no—
234#95—1461no—
235#95—1461no—
236#95—1461no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—731no—
240C22×C4—731no—
241C22×C4—731no—
242C22×C4—731no—
243C22×C4—1461no—
244C22×C4—1461no—
245C22×C4C2×C4×D7311yescharacteristic
246C22×C4D4×D7311yescharacteristic
247C22×C4D4×D7311yescharacteristic
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—2921no—
255C2×C8—2921no—
256C2×C8—2921no—
257C2×C8—2921no—
258C2×C8—1462no—
259C2×C8—1462no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—2921no—
263C4⋊C4—2921no—
264C4⋊C4—2922no—
265C4⋊C4—2922no—
266C4⋊C4—2922no—
267C4⋊C4—2922no—
268C42—2921no—
269C42—2921no—
270C42—2921no—
271C42—2921no—
272C42—2921no—
273C42—1462no—
274C42Q8×D7311yescharacteristic
275C42C2×Dic14611yescharacteristic
276C42#1192402711yescharacteristic
277C42#1192402811yescharacteristic
278C23C22⋊C4×D7311yescharacteristic
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—2921no—
292C2×C4—2921no—
293C2×C4—2921no—
294C2×C4—2921no—
295C2×C4—2921no—
296C2×C4—2921no—
297C2×C4—732no—
298C2×C4—1461no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4#1455655611yescharacteristic
310C2×C4C4×Dic14611yescharacteristic
311C2×C4#1455656811yescharacteristic
312C2×C4#1455656911yescharacteristic
313C2×C4#1455657711yescharacteristic
314C2×C4#1455659011yescharacteristic
315C8—42no—
316C8—42no—
317C8—2922no—
318C8—2922no—
319C22#1798849111yescharacteristic
320C22#1798856811yescharacteristic
321C22#1798857011yescharacteristic
322C22#104×D7311yescharacteristic
323C22#1798860211yescharacteristic
324C22#1798860211yescharacteristic
325C22#1798860211yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—2921no—
335C4—2921no—
336C4—2921no—
337C4—5841no—
338C4—5841no—
339C4—1462no—
340C2#2260853511yescharacteristic
341C2#2260855011yescharacteristic
342C2#2260855911yescharacteristic
343C2#2260856111yescharacteristic
344C2#2261087311yescharacteristic
345C2#2261091011yescharacteristic
346C2#2261092211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D73
commutatorC22×C4×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1295C2
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C42×C73C23
hypercenter#1295D73
hypocenterC73#9893
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
181. C73#9893semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226183162
#226097852
#226096792
#226078132
#226078122
C73×#12952
#989373